Fig. 3: The relaxed atomic structure and the GB energy of Ca/Si co-doped Σ13 M(Al) GB.

The structure model is viewed along the a \([11\bar{2}0]\) axis and b \([\bar{2}021]\) axis, where the structure model in a is overlaid on the ABF-STEM image. Al, O, Ca, and Si atoms are represented by the colors cyan and dark red, green, and light red, respectively. The structural tetrahedron (pale red) and octahedron (pale green) for Si and Ca are given in b. The scale bar in b is 2 Å, which applies to a. c The GB energy (J m⁻²) of Σ13 α-Al₂O₃ GB in an oxygen-rich atmosphere as functions of chemical potentials of Ca and Si. At maximum chemical potentials of Ca and Si, CaAl₄O₇ and Al₂SiO₅ are formed, respectively. d The cross-sectional view of the GB energy along the white line of A-X-B in c.